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Controllability of 3D incompressible Euler equationsby a finite-dimensional externalforce

Published online by Cambridge University Press:  02 July 2009

Hayk Nersisyan
Hayk Nersisyan*
Affiliation:
CNRS (UMR 8088), Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France. Hayk.Nersisyan@u-cergy.fr
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Abstract

In this paper, we study thecontrol system associated with the incompressible 3D Euler system.We show that the velocity field and pressure of the fluid areexactly controllable in projections by the same finite-dimensionalcontrol. Moreover, the velocity is approximately controllable. We also prove that 3D Eulersystem is not exactly controllable by a finite-dimensionalexternal force.

Keywords

Controllability3D incompressible Euler equationsAgrachev-Sarychev method
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 3 , July 2010 , pp. 677 - 694
Copyright
© EDP Sciences, SMAI, 2009

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